This invention relates to an image reconstruction method in nuclear magnetic resonance (NMR) imaging and in particular to an image reconstruction method in NMR imaging capable of realizing easily a high speed imaging by reducing the amplitude and the frequency of the oscillating gradient magnetic field used by the echo planar method by 50%.
The echo planar method is described in J. Phys. C: Solid State Physics 10, L55-8 (1977). By this method the following relationship; EQU G.sub.x =2MG.sub.y ( 1)
where M represents the size of an image matrix, is valid between the amplitude G.sub.x of the oscillating gradient magnetic field and the amplitude G.sub.y of the gradient magnetic field stationarily applied. (Here it is assumed that M.times.M pixels are contained in an image matrix.) Further it is assumed here that the sizes of the form of the field of view and that of a pixel are equal in the x and y directions are equal to each other.
It is said that G.sub.y should be usually about 2.times.10.sup.-3 T/m. Therefore, assuming M=128, G.sub.x =5.12.times.10.sup.-1 Wb/m.sup.3. In practice it is almost impossible to drive a gradient magnetic field having such a great amplitude.
On the other hand, in order to overcome this difficulty as described above, a method called fast Fourier imaging has been proposed in Magnetic Resonance in Medicine Vol. 2, pp. 203-217 (1985).
Using the echo planar method it is possible in principle to reconstruct an image by a single signal measurement succeeding an application of a 90.degree. pulse. On the other hand, in order to implement the Fourier imaging method M measurements are necessary. The fast Fourier imaging method provides a comprising method between the echo planar method and the Fourier imaging method. According to this method N measurements are necessary, N being given by 1.ltoreq.N.ltoreq.M. However the requirement for the amplitude of the gradient magnetic field, corresponding to Eq. (1), is alleviated to; ##EQU1## Adopting N=32 in the above numerical example, G.sub.x= 1.6.times.10.sup.-2 T/m. Even this value is fairly difficult to realize in practice. In order to reduce the required amplitude of the gradient magnetic field to a practical domain G.sub.x &lt;1.times.10.sup.-2 T/m, N=64 should be adopted in this numerical example, which is reduced only to a half of the number of measurements of 128 necessitated by the Fourier imaging method.